Finite Group Databasebeta

← #25014861

Subgroups — #25014861

Order 11008.

490 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583282C211yesmaximal, characteristic
2C2×#14582716C211yesmaximal, characteristic, complemented
3C2×#14582714C211yesmaximal, characteristic, complemented
4C2×#14582712C211yesmaximal, characteristic
5M32×Dic43C211yesmaximal, characteristic, complemented
6#19134765C211yesmaximal, characteristic, complemented
7C2×C43×#361C211yesmaximal, characteristic
8C22×Dic172C2211yescharacteristic
9C22×#10621883—21no—
10C2×#13063312—21no—
11C2×#13063265C2211yescharacteristic
12#14583282—21no—
13#14583282—21no—
14#14583282C412yes—
15#14583282C412yes—
16C2×#13063261C2211yescharacteristic
17C2×#13063260—21no—
18#14582922—21no—
19C2×C8×Dic43C2211yescharacteristic
20#14582716—22no—
21#14582714—22no—
22#14582712—22no—
23#14582674—21no—
24C16×Dic43—21no—
25C22×D8×C43C2211yescharacteristic
26C2×M32×C43C2211yescharacteristic
27C2×#108×C43C2211yescharacteristic
28C43×#361—22no—
29C22×Dic86—21no—
30C2×Dic172—21no—
31C2×Dic172—21no—
32C2×Dic172—21no—
33C2×Dic172—21no—
34C2×Dic172—21no—
35C2×Dic172C2×C412yes—
36C2×#10621883—22no—
37C2×#10621883—22no—
38C2×#10621883—42no—
39C2×#10621883—42no—
40C2×#10621877—21no—
41C22×C43⋊C8D411yescharacteristic
42#13063312—22no—
43#13063312—22no—
44#13063312—42no—
45C2×C22⋊Dic43—42no—
46C2×C4×Dic43D411yescharacteristic
47#13063265—21no—
48#13063265D412yes—
49C2×C43⋊C16—21no—
50#13063261—21no—
51#13063261—21no—
52#13063260—42no—
53Dic43⋊C8—42no—
54C8×Dic43C2×C411yescharacteristic
55C8×Dic43C2×C411yescharacteristic
56C8×Dic43D411yescharacteristic
57C8×Dic43D411yescharacteristic
58C22×D4×C43—21no—
59C2×D8×C43—21no—
60C2×D8×C43—21no—
61C2×D8×C43—21no—
62C2×D8×C43—21no—
63C2×D8×C43—21no—
64C2×D8×C43C2×C412yes—
65C2×M16×C43—21no—
66C22×C8×C43C2311yescharacteristic
67M32×C43—21no—
68M32×C43D412yes—
69C2×C16×C43—21no—
70#108×C43—21no—
71#108×C43—21no—
72C24×C43—41no—
73C2×D4×C43—22no—
74C2×D4×C43—41no—
75C2×D4×C43—41no—
76C2×D4×C43—41no—
77C2×D4×C43—41no—
78C2×D4×C43—41no—
79C22×C4×C43C2×D411yescharacteristic
80C22×Dic43—41no—
81C22×Dic43SD1612yes—
82C2×Dic86—22no—
83C2×Dic86—41no—
84C2×Dic86—41no—
85C2×Dic86—41no—
86C2×Dic86—41no—
87C2×Dic86—41no—
88D8×C43—22no—
89D8×C43—22no—
90D8×C43—41no—
91D8×C43—41no—
92M16×C43—41no—
93M16×C43—41no—
94C2×C8×C43—41no—
95C2×C8×C43C22×C411yescharacteristic
96C2×C8×C43C2×D411yescharacteristic
97C2×C8×C43C2×D411yescharacteristic
98C2×C8×C43C2×D411yescharacteristic
99C2×C8×C43#4111yescharacteristic
100C2×C8×C43#4111yescharacteristic
101C22⋊Dic43—44no—
102C22⋊Dic43—44no—
103#10621883—44no—
104#10621883—44no—
105C4×Dic43C22⋊C411yescharacteristic
106C4×Dic43C22⋊C411yescharacteristic
107C4×Dic43D812yes—
108#10621877—41no—
109#10621877—41no—
110C2×C43⋊C8—41no—
111C2×C43⋊C8C22⋊C411yescharacteristic
112C2×C43⋊C8C22⋊C411yescharacteristic
113C2×C43⋊C8D812yes—
114C2×C43⋊C8SD1612yes—
115Dic172—22no—
116Dic172—22no—
117Dic172—41no—
118Dic172—41no—
119C16×C43—22no—
120C43⋊C16—22no—
121C23×C43—42no—
122C23×C43—84no—
123C23×C43—81no—
124C23×C43—81no—
125C23×C43C2×SD1611yescharacteristic
126D4×C43—42no—
127D4×C43—42no—
128D4×C43—81no—
129D4×C43—81no—
130C2×C4×C43C2×C22⋊C411yescharacteristic
131C2×C4×C43#12411yescharacteristic
132C2×C4×C43#12711yescharacteristic
133C2×C4×C43C2×D811yescharacteristic
134C2×C4×C43C2×D811yescharacteristic
135C2×C4×C43C2×SD1611yescharacteristic
136C2×Dic43—42no—
137C2×Dic43—42no—
138C2×Dic43—81no—
139C2×Dic43—81no—
140C2×Dic43#10212yes—
141C2×Dic43#10212yes—
142Dic86—42no—
143Dic86—42no—
144Dic86—81no—
145Dic86—81no—
146C8×C43—81no—
147C8×C43C4×D411yescharacteristic
148C8×C43C4×D411yescharacteristic
149C8×C43#12111yescharacteristic
150C8×C43#12111yescharacteristic
151C43⋊C8—81no—
152C43⋊C8#10212yes—
153C43⋊C8#10212yes—
154#13214—431nomaximal, Sylow
155C22×C43—22no—
156C22×C43—84no—
157C22×C43—82no—
158C22×C43—162no—
159C22×C43—162no—
160C22×C43C2×#10211yescharacteristic
161C22×C43#48611yescharacteristic
162C22×C43#49211yescharacteristic
163C4×C43#39011yescharacteristic
164C4×C43C2×#10211yescharacteristic
165C4×C43#48611yescharacteristic
166C4×C43#49311yescharacteristic
167Dic43—22no—
168Dic43—22no—
169Dic43—82no—
170C2×#495—431no—
171C2×#362—431no—
172C2×#362—431no—
173C2×#361—431no—
174C2×#361D4311yescharacteristic
175C4×M32—431no—
176#1848—431no—
177C2×C43—21no—
178C2×C43—21no—
179C2×C43—162no—
180C2×C43#195711yescharacteristic
181C2×C43#214812yes—
182C22×Q16—431no—
183C22×SD16—861no—
184C22×D8C2×D4311yescharacteristic
185C2×#124—861no—
186C2×M32—431no—
187C2×M32C2×D4311yescharacteristic
188#495—432no—
189#495—432no—
190#495—861no—
191#495—861no—
192C2×#108—431no—
193C2×#108—861no—
194C2×#108C2×D4311yescharacteristic
195#423—861no—
196C2×C4×C8—431no—
197#362—862no—
198#362—862no—
199#361—22no—
200#361—862no—
201#346—861no—
202C4×C16—861no—
203C43#1321411yescharacteristic, complemented, Sylow
204C22×Q8—861no—
205C22×D4—21no—
206C2×Q16—432no—
207C2×Q16—861no—
208C2×Q16—861no—
209C2×Q16—861no—
210C2×Q16—861no—
211C2×Q16—861no—
212C2×SD16—862no—
213C2×SD16—862no—
214C2×SD16—1722no—
215C2×SD16—1722no—
216C2×D8—21no—
217C2×D8—21no—
218C2×D8—21no—
219C2×D8—21no—
220C2×D8—21no—
221C2×D8C4×D4312yes—
222C2×M16—21no—
223C2×M16—861no—
224C22×C8—431no—
225C22×C8C22×D4311yescharacteristic
226#124—862no—
227#124—862no—
228#124—1722no—
229C2×C22⋊C4—1722no—
230C2×C42—431no—
231M32—21no—
232M32—432no—
233M32—861no—
234M32C22⋊D4312yes—
235C2×C16—21no—
236C2×C16—861no—
237#108—21no—
238#108—21no—
239#108—861no—
240#108—861no—
241#108—1722no—
242C4⋊C8—1722no—
243C4×C8—431no—
244C4×C8—431no—
245C4×C8—431no—
246C4×C8—431no—
247C24—41no—
248C2×Q8—862no—
249C2×Q8—1721no—
250C2×Q8—1721no—
251C2×Q8—1721no—
252C2×Q8—1721no—
253C2×Q8—1721no—
254C2×D4—22no—
255C2×D4—41no—
256C2×D4—41no—
257C2×D4—41no—
258C2×D4—41no—
259C2×D4—41no—
260C22×C4—432no—
261C22×C4—1721no—
262C22×C4D4×D4311yescharacteristic
263Q16—862no—
264Q16—862no—
265Q16—1721no—
266Q16—1721no—
267SD16—1724no—
268SD16—1724no—
269D8—22no—
270D8—22no—
271D8—41no—
272D8—41no—
273M16—41no—
274M16—41no—
275M16—1721no—
276M16—1721no—
277C2×C8—41no—
278C2×C8—431no—
279C2×C8—431no—
280C2×C8—432no—
281C2×C8—432no—
282C2×C8—1721no—
283C2×C8C2×C4×D4311yescharacteristic
284C2×C8#1062189811yescharacteristic
285C2×C8D4×D4311yescharacteristic
286C2×C8D4×D4311yescharacteristic
287C2×C8#1062190011yescharacteristic
288C2×C8C2×C22⋊D4311yescharacteristic
289C22⋊C4—1724no—
290C22⋊C4—1724no—
291C42—431no—
292C42—431no—
293C42—432no—
294C16—22no—
295C16—862no—
296C23—42no—
297C23—84no—
298C23—81no—
299C23—81no—
300C23SD16×D4311yescharacteristic
301Q8—3441no—
302Q8—3441no—
303Q8—1722no—
304Q8—1722no—
305D4—42no—
306D4—42no—
307D4—81no—
308D4—81no—
309C2×C4—432no—
310C2×C4—432no—
311C2×C4—3441no—
312C2×C4—3441no—
313C2×C4—1722no—
314C2×C4—1722no—
315C2×C4C22⋊C4×D4311yescharacteristic
316C2×C4#1306331111yescharacteristic
317C2×C4#1306332111yescharacteristic
318C2×C4D8×D4311yescharacteristic
319C2×C4D8×D4311yescharacteristic
320C2×C4SD16×D4311yescharacteristic
321C8—81no—
322C8—432no—
323C8—432no—
324C8—3441no—
325C8(C22⋊D43)⋊C411yescharacteristic
326C8C4×C22⋊D4311yescharacteristic
327C8#1306329711yescharacteristic
328C8#1306329811yescharacteristic
329C22—22no—
330C22—84no—
331C22—82no—
332C22—162no—
333C22—162no—
334C22#102×D4311yescharacteristic
335C22#1458324411yescharacteristic
336C22#1458327011yescharacteristic
337C4—862no—
338C4—862no—
339C4—3442no—
340C4#1458279911yescharacteristic
341C4#102×D4311yescharacteristic
342C4#1458324411yescharacteristic
343C4#1458327411yescharacteristic
344C2—21no—
345C2—21no—
346C2—162no—
347C2#1913539911yescharacteristic
348C2#1913634112yes—
subgroupG/H
centerC22#102×D43
commutatorC2×C8×C43C22×C4
FrattiniC22×C8C22×D43
FittingC2×C43×#361C2
socleC22×C43C2×#102
prime radicalC22×D8×C43C22
cosocleC22×C8×C43C23
hypercenterC2×#361D43
hypocenterC43#13214
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#361

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×#14582716C2semidirect
3. C2×#14582714C2semidirect
5. M32×Dic43C2semidirect
6. #19134765C2semidirect
203. C43#13214semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#145832822
C2×#145827162
C2×#145827142
C2×#145827122
M32×Dic432
#191347652
C2×C43×#3612
#1321443